If the two straight lines, $y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}$ are perpendicular to each other, then $m_{1} m_{2} =$ ____

- 1

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\frac{1}{2}

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Solution

The correct option is A $- 1$
Since the slope of perpendicular lines are the negative reciprocals of each other and a pair of these lines intersects at $90$ degrees.

Here, the slope of $y_{1} = m_{1} x + c_{1}$ is $m_{1}$ and the slope of $y_{2} = m_{2} x + c_{2}$ is $m_{2}$ and these two lines are perpendicular, then the product of the slopes is $- 1$ .

Hence, $m_{1} \times m_{2} = - 1$

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Similar questions

Q. If the two straight lines

y = m_{1} x + c_{1}

and

y = m_{2} x + c_{2}

are perpendicular to each other then

m_{1} m_{2} =

_____________

Q. If three lines whose rquation are

y = m_{1} x + c_{1}, y = m_{2} x + c_{2}

and

y = m_{2} x + c_{2}

concurrent, then show that

m_{1} (c_{2} - c_{1}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0

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$m_{1} (c_{2} - c_{3}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0$

Q. If

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and

y + 3 = m_{2} (x + 2)

are two tangents to the parabola

y^{2} = 8 x

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m_{1} m_{2} = - 1

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If the two straight lines, y=m1x+c1 and y=m2x+c2 are perpendicular to each other, then m1m2= ____

If the two straight lines, $y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}$ are perpendicular to each other, then $m_{1} m_{2} =$ ____